Screen LibraryBifurcation and chaos in complex systems /
Presents the achievements on bifurcation studies of nonlinear dynamical systems. This book deals with the fundamental theoretical issues of bifurcation analysis in smooth and non-smooth dynamical systems. The cell mapping methods are presented for global bifurcations in stochastic and deterministic,...
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| Corporate Authors: | |
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| Group Author: | ; |
| Published: |
Elsevier,
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| Publisher Address: | Amsterdam : |
| Publication Dates: | 2006. |
| Literature type: | eBook |
| Language: | English |
| Series: |
Edited series on advances in nonlinear science and complexity ; v. 1. 1574-6909 |
| Subjects: | |
| Online Access: |
http://www.sciencedirect.com/science/bookseries/15746909/1 |
| Summary: |
Presents the achievements on bifurcation studies of nonlinear dynamical systems. This book deals with the fundamental theoretical issues of bifurcation analysis in smooth and non-smooth dynamical systems. The cell mapping methods are presented for global bifurcations in stochastic and deterministic, nonlinear dynamical systems. |
| Carrier Form: | 1 online resource (xii, 388 pages) : illustrations (1 color). |
| Bibliography: | Includes bibliographical references and indexes. |
| ISBN: |
0080462669 9780080462660 |
| Index Number: | QA380 |
| CLC: | O177.91 |
| Contents: | Cover Dedication Preface Contents Bifurcation, Limit Cycle and Chaos of Nonlinear Dynamical Systems -- Introduction -- Bifurcation of limit cycles -- -- Lifting 2-D model with delayed feedback control -- -- Internet congestion model -- -- Hilbert's 16th problem -- Bifurcation control and chaos synchronization -- -- Global ultimate boundedness of chaotic systems -- -- Hopf bifurcation control -- -- Tracking and chaos synchronization -- Competitive modes -- -- Definition of CM -- -- Application of CM: estimating chaotic parameter regimes -- -- Application of CM: constructing new chaotic systems -- Conclusions -- Acknowledgement -- References Grazing Flows in Discontinuous Dynamic Systems -- Introduction -- Domain accessibility -- Discontinuous dynamic systems -- Oriented boundary and singular sets -- Local singularity and grazing flows -- Piecewise linear systems -- Friction-induced oscillators -- Conclusions -- Appendix -- References Global Bifurcations of Complex Nonlinear Dynamical Systems with Cell Mapping Methods -- Introduction -- Cell mapping methods -- -- Simple cell mapping -- -- Generalized cell mapping -- Crises in deterministic systems -- -- A chaotic boundary crisis -- -- Chaotic boundary and interior crises -- -- Wada fractal boundary and indeterminate crisis -- -- Double crises -- Bifurcations of nonlinear systems with small random disturbances -- -- Logistic map with random coefficients -- -- A two-dimensional random map -- -- Duffing oscillator with small random excitations -- -- Noisy crisis in a twin-well Duffing system -- Fuzzy bifurcations -- -- Fuzzy generalized cell mapping -- -- Bifurcation of one-dimensional fuzzy systems -- -- Bifurcation of fuzzy nonlinear oscillators -- -- Conjectures -- Effect of bifurcation on semiactive optimal controls -- -- Optimal control problem -- -- Saddle-node bifurcation -- -- Supercritical Pitchfork bifurcation -- -- Subcritical Hopf bifurcation -- References Bifurcation Analysis of Nonlinear Dynamic Systems with Time-Periodic Coefficients -- Introduction -- Formulation of the problem -- Local stability and conditions for bifurcations: Floque t theory -- Lyapunov-Floque t transformation -- Nonlinear analysis -- -- Time-periodic center manifold reduction -- -- Time-dependent normal form theory -- -- Versal deformation of the normal form -- -- Solution in the original (physical) variables -- The codimension one bifurcations -- -- Flip bifurcation -- -- Transcritical and symmetry breaking bifurcations -- -- Cyclic fold bifurcation -- -- Secondary Hopf bifurcation -- Applications -- -- A system with an exact solution: an example of the flip bifurcation -- -- A system with a small parameter: a comparison with averaging method -- -- A simple pendulum with periodic base excitation: an example of the symmetry breaking bifurcation -- -- An example of the secondary Hopf bifurcation: a double inverted pendulum with a periodic follower load -- Summary and conclusions -- References Modal Interactionsmodal interactions in Asymmetric Vibrations of Circular Platescircular plates -- Introduction -- Governing equations -- Solution -- Steady-state responses and numerical examples -- -- The plate without elastic foundation (K = 0): the case of no internal resonance -- -- The plate on elastic foundation (K> 0): the case of internal resonance (omegaNM 3?CD, where N = 3C) -- -- The plate on elastic foundation (K> 0): the case of internal resonance (?NM 3?CD, where N = C) -- Appendix A -- Appendix B -- -- Case 1:?32 3?11 and??11 -- -- Case 2:?32 3?11 and??32 -- Appendix C -- References List of Contributors Author Index Subject Index Last Page. |